But inelastic collision are where KE is transferred into other forms of energy (e.g sound) so how could another object's velocity reach the same level as what the first object achieved if not all KE is transferred
Momentum = mv
Kinetic Energy = 1/2mv^2
Whilst you can have negative momentum, it is the opposite for kinetic energy (because velocity will always be squared)
Example: Assume there are two toy cars. Car A (mass 1 kg) travelling towards Car B at 2 m/s to the right, whilst Car B (mass 3kg) is travelling towards it at 3 m/s to the left (Notice the differences in mass). After collision Car A travels 1 m/s to the left, and Car B travels 2 m/s to the left. (Assume right is positive)
Momentum.
Initial momentum of the system:
Car A: p = mv = 2 kg m/s
Car B: p = mv = -9 kg m/s
initial momentum = -7 kg m/s
final momentum
Car A: p = mv = -1 kg m/s
Car B: p = mv = -6 kg m/s
final momentum of system = -7 kg m/s
Therefore momentum is conserved.
Now as for kinetic energy within the system
initial kinetic energy = 0.5 x 1 x 2^2 + 0.5 x 2 x (-3)^2
= 11 J
final kinetic energy = 0.5 x 1 x (-1)^2 + 0.5 x 2 x (-2)^2
= 4.5 J
Ke is lost, therefore this is an inelastic collision (its being converted to heat, sound etc...).
When I said that if one object loses velocity, and the other gains it, it doesn't necessarily have to be the same amount (So in this case, Car B becomes slower by 1 m/s, but Car A did not "gain" that 1 m/s, instead it's change in velocity was -3 m/s). Mass plays a major role in determining its final velocity after collision.
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